<-- Enter p
<-- Enter number of trials
 

Simulate 20 bernoulli trials with:

a success probability p = 0.75

Bernoulli Trial Formula

pkqn - k
where p = success probability, q = 1 - p

Bernoulli Trial Table

Trial #Success/FailureMath Work 1Math Work 2Probability
1Success0.7510.25(1 - 1)0.75 x 10.75
2Success0.7510.25(1 - 1)0.75 x 10.75
3Success0.7510.25(1 - 1)0.75 x 10.75
4Failure0.7500.25(1 - 0)1 x 0.250.25
5Failure0.7500.25(1 - 0)1 x 0.250.25
6Failure0.7500.25(1 - 0)1 x 0.250.25
7Success0.7510.25(1 - 1)0.75 x 10.75
8Failure0.7500.25(1 - 0)1 x 0.250.25
9Success0.7510.25(1 - 1)0.75 x 10.75
10Success0.7510.25(1 - 1)0.75 x 10.75
11Success0.7510.25(1 - 1)0.75 x 10.75
12Failure0.7500.25(1 - 0)1 x 0.250.25
13Success0.7510.25(1 - 1)0.75 x 10.75
14Failure0.7500.25(1 - 0)1 x 0.250.25
15Success0.7510.25(1 - 1)0.75 x 10.75
16Success0.7510.25(1 - 1)0.75 x 10.75
17Success0.7510.25(1 - 1)0.75 x 10.75
18Success0.7510.25(1 - 1)0.75 x 10.75
19Success0.7510.25(1 - 1)0.75 x 10.75
20Success0.7510.25(1 - 1)0.75 x 10.75

Compare Expected to Actual Results:

Given your success probability of 0.75:
we expect 0.75 x 20 = 15 successes

Our actual results were 14 successes and 6 failures

Calculate the median:


Since q < p, 0.25 < 0.75, then our median is 1

Calculate Variance:

Variance σ2 = pq or p(1 - p)

Variance σ2 = (0.75)(0.25)

Variance σ2 = 0.1875

Calculate Skewness:

Skewness  =  q - p
  pq

Skewness  =  0.25 - 0.75
  (0.75)(0.25)

Skewness  =  -0.5
  0.1875

Skewness  =  -0.5
  0.43301270189222

Skewness = -1.1547005383793

Calculate Kurtosis:

Kurtosis  =  1 - 6pq
  pq

Kurtosis  =  1 - 6(0.75)(0.25)
  (0.75)(0.25)

Kurtosis  =  1 - 6(0.1875)
  0.1875

Kurtosis  =  1 - 1.125
  0.1875

Kurtosis  =  -0.125
  0.1875

Kurtosis = -0.66666666666667

Calculate Entropy:

Entropy = -qLn(q) - pLn(p)

Entropy = -(0.25)Ln(0.25) - 0.75Ln(0.75)

Entropy = -(0.25)(-1.3862943611199) - 0.75(-0.28768207245178)

Entropy = -(-0.34657359027997) - -0.21576155433884

Entropy = -0.034238445661164

Answer Summary:

Probability = 0.75
Median = 1
Variance = 0.1875
Skewness = -1.1547005383793
Kurtosis = -0.66666666666667
Entropy = -0.034238445661164





What is the Answer?
Probability = 0.75
Median = 1
Variance = 0.1875
Skewness = -1.1547005383793
Kurtosis = -0.66666666666667
Entropy = -0.034238445661164
How does the Bernoulli Trials Calculator work?
Free Bernoulli Trials Calculator - Given a success probability p and a number of trials (n), this will simulate Bernoulli Trials and offer analysis using the Bernoulli Distribution. Also calculates the skewness, kurtosis, and entropy
This calculator has 2 inputs.

What 3 formulas are used for the Bernoulli Trials Calculator?

pkqn - k
p = success probability
q = 1 - p

For more math formulas, check out our Formula Dossier

What 9 concepts are covered in the Bernoulli Trials Calculator?

bernoulli trials
Repeating an experiment using a bernoulli distribution
expected value
predicted value of a variable or event
E(X) = ΣxI · P(x)
kurtosis
statistical measure describing the distribution, or skewness, of observed data around the mean. Also referred to as the volatility of volatility
mean
A statistical measurement also known as the average
median
the value separating the higher half from the lower half of a data sample,
probability
the likelihood of an event happening. This value is always between 0 and 1.
P(Event Happening) = Number of Ways the Even Can Happen / Total Number of Outcomes
skewness
measure of the asymmetry of the probability distribution of a real-valued random variable about its mean
trial
a single performance of well-defined experiment
variance
How far a set of random numbers are spead out from the mean
Example calculations for the Bernoulli Trials Calculator
Bernoulli Trials Calculator Video

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